The Tortoise’s mind needs the dynamic of adding Y to the belief pool when X and (X→Y) are previously in the belief pool. If this dynamic is not present—a rock, for example, lacks it—then you can go on adding in X and (X→Y) and (X⋀(X→Y))→Y until the end of eternity, without ever getting to Y.
The phrase that once came into my mind to describe this requirement, is that a mind must be created already in motion. There is no argument so compelling that it will give dynamics to a static thing. There is no computer program so persuasive that you can run it on a rock.
And this (I then replied) relies on the notion that by unwinding all arguments and their justifications, you can obtain an ideal philosophy student of perfect emptiness, to be convinced by a line of reasoning that begins from absolutely no assumptions.
But who is this ideal philosopher of perfect emptiness? Why, it is just the irreducible core of the ghost!
And that is why (I went on to say) the result of trying to remove all assumptions from a mind, and unwind to the perfect absence of any prior, is not an ideal philosopher of perfect emptiness, but a rock. What is left of a mind after you remove the source code? Not the ghost who looks over the source code, but simply… no ghost.
So—and I shall take up this theme again later—wherever you are to locate your notions of validity or worth or rationality or justification or even objectivity, it cannot rely on an argument that is universally compelling to all physically possible minds.
The idea clone of saturn stated is discussed in the sequences, in Created Already In Motion:
And in No Universally Compelling Arguments: